According to Dell Optiplex 7040M manual, the system is supported up to 32GB memory configuration (2x16GB, dual channels, DDR4 DIMM. Had any one ever upgraded the system Optiplex,7040 Micro with 2x16GB DIMMs. It was very confusing since the earlier spec says it supports up to 16GB while the latest manual version says it supports 32GB memory configuration.

https://www.dell.com/support/manuals/us/en/04/optiplex-7040-desktop/opti7040m_om/installing-the-memory-module?guid=guid-89fb4f41-39a4-424c-ad10-2b96ddfbbfd7&lang=en-us

Open the PDF file and read the Max memory configuration.